258
Y. He et al.
Fig. 20.5 Pareto optimal
fronts
index for crossover and mutation are 10 and 20. The fitness function and constrains
function can be determined by the Kriging metamodels above.
20.5.3 Result Analysis
The POF of the NSGA-II based on Kriging surrogate model is shown in Fig. 20.5.
Refer to Fig. 20.4, the Pareto optimal front of NSGA-II based on the Kriging model
performs well in convergence and diversity.
In real engineering optimization design, the lightweight is as important as the
crashworthiness. Therefore, one of the optimal points in POF was determined as the
optimum solution. Then the optimum solution is compared to baseline model and
the accuracy is verified by calculating the objective values in FE model, the results
are shown in Table 20.4.
To compare the optimum results in FE models, the deformation of the front rail
in frontal impact test against deformable barrier with 40% overlapping in Ls-Dyna
software are shown in Fig. 20.6. It is obvious that the optimized front rail has smaller
deformation after impact.
20.6 Conclusion
In order to obtain the optimum structure of the parts in front rail, a surrogate-based
optimization is developed a frontal rail. The multi-optimization problem is defined to
minimum the peak accelerate a max and the mass of frontal rail m with the constraints
of the rearward intrusions of A-pillar D 1 and the steering column D 2 .To reduce the
calculation time, the Kriging surrogate model is proposed to provide high accuracy
Y. He et al.
Fig. 20.5 Pareto optimal
fronts
index for crossover and mutation are 10 and 20. The fitness function and constrains
function can be determined by the Kriging metamodels above.
20.5.3 Result Analysis
The POF of the NSGA-II based on Kriging surrogate model is shown in Fig. 20.5.
Refer to Fig. 20.4, the Pareto optimal front of NSGA-II based on the Kriging model
performs well in convergence and diversity.
In real engineering optimization design, the lightweight is as important as the
crashworthiness. Therefore, one of the optimal points in POF was determined as the
optimum solution. Then the optimum solution is compared to baseline model and
the accuracy is verified by calculating the objective values in FE model, the results
are shown in Table 20.4.
To compare the optimum results in FE models, the deformation of the front rail
in frontal impact test against deformable barrier with 40% overlapping in Ls-Dyna
software are shown in Fig. 20.6. It is obvious that the optimized front rail has smaller
deformation after impact.
20.6 Conclusion
In order to obtain the optimum structure of the parts in front rail, a surrogate-based
optimization is developed a frontal rail. The multi-optimization problem is defined to
minimum the peak accelerate a max and the mass of frontal rail m with the constraints
of the rearward intrusions of A-pillar D 1 and the steering column D 2 .To reduce the
calculation time, the Kriging surrogate model is proposed to provide high accuracy